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Abstract
We numerically demonstrate a switchable broadband terahertz spatial modulator composed of ginkgo-leaf-patterned graphene and transition material vanadium dioxide (VO2). The phase transition property of VO2 is used to switch the spatial modulator from absorption mode to transmission mode, and the graphene behaves as dynamically adjustable material for a large scale of absorption and transmittance modulation. When VO2 is in the metallic state and the Fermi energy of graphene is set as 0.8 eV, the proposed modulator behaves as a broadband absorber with the absorbance over 85% from 1.33 to 2.83 THz. By adjusting the graphene Fermi level from 0 to 0.8 eV, the peak absorbance can be continuously tuned from 24.3% to near 100% under the absorption mode, and the transmittance at 2.5 THz can be continuously tuned from 87% to 35.5% under the transmission mode. To further increase the bandwidth, a three-layer-patterned-graphene is introduced into a new modulator design, which achieves a wide bandwidth of 3.13 THz for the absorbance over 85%. By the combination of the tunability of graphene and VO2, the proposed modulators not only can flexibly switch between dual-functional modulation modes of absorption and transmission but also possess deep modulation depth. Benefitting from the excellent modulation performance, the proposed switchable dual-functional spatial modulators may offer significant potential applications in various terahertz smart optoelectronic devices.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz waves have many applications in wireless communication, imaging [1], spectroscopy [2], sensing [3], etc. For many applications, efficient terahertz devices such as waveguides, filters, modulators, detectors are highly desirable. Among these devices, terahertz modulators play a crucial role in terahertz interconnections, signal processing, imaging, which have attracted increasing attention in recent years. Metamaterials are artificially structured materials that can be used to manipulate electromagnetic waves in the microwave, terahertz, optical regions. For example, metamaterial-based absorbers with periodic square rings, cross/hash-shaped resonators, circular split rings were proposed to achieve single narrowband [4–5], dual-band [6–7], multi-band [8–9] and broadband [10–11] absorption. Multiple adjacent resonators in a single unit cell [12], multilayer structure [13], combined super unit cell [14] have been introduced into the metamaterial absorbers to broaden the absorption bandwidth. Metamaterial-based electromagnetically induced transparency can be achieved by quantum interference between bright and dark modes [15], or by bright-bright mode coupling [16], which can form narrow and high quality factor transparency peaks for sensing applications. Besides, many dual-band, multiband, and broadband polarization converters based on metamaterials have also been proposed [17–19]. However, since these metamaterial devices are composed of normal metallic and dielectric materials, their absorption, reflection, and transmission characteristics cannot be adjustable after fabrication, which severely restricted their applications in many optoelectronic devices. Recently, tunable elements or materials like diodes, varactors, MEMS, GaAs, perovskite, graphene, and VO2 provide a new way to design terahertz modulators and other adjustable metamaterial devices with great flexibility under specific external stimuli.
Graphene is a two-dimensional honeycomb structure consisting of one monolayer of carbon atoms [20]. It is applied widely in tunable devices due to its excellent electrical and optical properties by changing the chemical or electrical doping [21–22]. Recently, various graphene absorbers [23–27], modulators [28–32] including waveguide modulators, spatial modulators and wavefront modulators have been investigated. To further increase the field confinement effect and modulation performance, graphene/metal and graphene/dielectric hybrid plasmonic waveguide modulators have also been demonstrated [33–34]. On the other hand, many terahertz spatial modulators have also been demonstrated. For example, Sensale-Rodriguez et al. experimentally demonstrated a broadband graphene terahertz spatial modulator with a modulation depth of 15% and a modulation rate of 10 kHz [35]. To improve the absorption, transmission, or reflection modulation depth and rate, several spatial modulator designs with graphene-based metamaterials have been investigated [36–38]. Despite the recent progress, most of these graphene spatial modulators only operate in single modulation mode with a limited modulation depth. Vanadium dioxide (VO2) is a promising phase transition material for electronics. Its unique metal-insulator transition behavior makes it switchable from an insulator to a conductor, enabling a significant conductivity change by five orders of magnitude under different electrical, thermal, and optical pathways [39–43]. Recently, VO2 has been used to design the new generation of tunable electronic devices, such as resonant absorbers [44], modulators [45], and frequency reconfigurable filters [46]. However, all of the devices mentioned above are composed of single flexible material, graphene, or VO2, which limits their capability in achieving multifunction such as tunable transparency, attenuation, and modulator in the same structure. A combination of two tunable metamaterials graphene and VO2 in one metamaterial device may enable the device to achieve dual/multi-mode simultaneously and enhance the tunability performance significantly.
In this paper, a switchable broadband terahertz spatial modulator composed of hybrid ginkgo-leaf-patterned graphene and vanadium dioxide is proposed to realize dual-functional modulation modes between absorption and transmission. In this design, the phase transition material VO2 acts as a switch for these two modulation modes. The maximum absorbance and transmittance modulation depth of 84.8% and 59.2% are achieved as the graphene Fermi level increases from 0 to 0.8 eV. To further increase bandwidth, we propose a three-layer patterned graphene structure based on the original modulator with a wide bandwidth of 3.13 THz is achieved for the absorbance over 85%. Generally, compared with conventional modulators based only on single tunable material graphene or VO2, the proposed spatial modulators show advantages of switchable dual modulation modes and better performance, which may have some potential applications in various terahertz smart optoelectronic devices.
2. Design and methods
The unit cell schematic diagram of the proposed switchable broadband terahertz spatial modulator integrated with ginkgo-leaf patterned graphene and VO2 is showed as Fig. 1. The modulator is a multi-layer structure with a ginkgo-leaf patterned graphene-dielectric spacer-gating layer-dielectric spacer-VO2 layer from top to bottom. Here, the ginkgo-leaf patterned graphene is employed to realize a broadband modulation performance. The dielectric spacer and grating layers are assumed to be a lossless polyethylene cyclic olefin copolymer (Topas) with a relative permittivity of ɛd = 2.35 and a lossless polysilicon layer with a relative permittivity of ɛg = 3 respectively [25–27,47]. The geometric parameters of the spatial modulator are set as follows, m = 2 µm, h = 25 µm, t1 = t2 = 0.02 µm, p = 56 µm, s = 0.1 µm. The absorption and transmission characteristics of the modulator can be tunable by controlling the conductivity of graphene and the metal-insulator transition behavior of VO2. The proposed modulator may be fabricated by using the state-of-the-art nanofabrication technology. In particular, the 20 nm Topas thin-film can be spin-coated in a spinner, the VO2 film can be produced using pulsed laser deposition (PLD), and the large-scale ginkgo-leaf patterned graphene can be produced through graphene synthesis, transfer, and electron beam lithography [48–55].
Fig. 1. (a) 3D schematic diagram of the proposed spatial modulator. (b) Top view of the proposed spatial modulator.
In this design, graphene is modeled as a 0-thick 2D surface impedance layer with Zg = 1/σg, where σg = σintra + σinter is the surface conductivity from the Kubo formula [53–55],
Fig. 2. (a) and (b) are the real and imaginary parts of graphene surface impedance under different chemical potentials, respectively. (c) and (d) are the real and imaginary parts of VO2 relative permittivity under different conductivity, respectively.
The relative permittivity of transition material VO2 can be modeled by using the Drude formula in the terahertz range as ${\varepsilon _{\textrm{V}{\textrm{O}_\textrm{2}}}}(\omega )= {\varepsilon _\infty } - \frac{{\omega _p^2({{\sigma_{\textrm{V}{\textrm{O}_\textrm{2}}}}} )}}{{{\omega ^2} + i\omega \gamma }}$ [56–57], where the damping frequency γ = 5.75×1013 s−1, the relative permittivity at the infinite frequency ${\varepsilon _\infty }$ = 12, the plasma frequency $\omega _p^2({{\sigma_{\textrm{V}{\textrm{O}_\textrm{2}}}}} )\textrm{ = }\frac{{{\sigma _{\textrm{V}{\textrm{O}_\textrm{2}}}}}}{{{\sigma _\textrm{0}}}}\omega _p^2({{\sigma_\textrm{0}}} )$, ${\sigma _\textrm{0}}$ = 3×105 S/m, and ${\omega _p}\left( {{\sigma _0}} \right)$ = 1.4×1015 rad/s. Since the conductivity of VO2 can be changed by five orders of magnitude from the insulating state to the metallic state [43], here, the VO2 conductivity is assumed to be ranging from ${\sigma _{\textrm{V}{\textrm{O}_\textrm{2}}}}$ = 10 S/m to ${\sigma _{{\rm{V}}{{\rm{O}}_{\rm{2}}}}}$ = 200000 S/m. Figures 2(c) and 2(d) show the dependence of the real and imaginary parts of VO2 relative permittivity on different VO2 conductivity. It is noted that the sign of Re(ɛVO2) varies from positive to negative, and the Im(ɛVO2) increases significantly when VO2 switches from the insulating state (10 S/m) to metallic state (200000 S/m).
In this work, we simulate the spatial modulator unit cell by assigning the periodic boundaries in both x- and y-directions, and Floquet ports in the z-direction under transverse electric (TE) polarization, where the polarization of incident terahertz wave is along y-axis under normal incidence. The absorbance is calculated by A = 1 – R – T, where the reflectance R =|S11|2 and the transmittance T = |S21|2. Since the proposed unit cell possesses the fourfold symmetry, the reflectance, transmittance, and absorbance of the modulator under TE and TM polarizations should be the same, and therefore, we only focus on the modulator performance discussion under TE polarized incidence.
3. Results and discussion
The modulation characteristics of the proposed terahertz spatial modulator can be achieved by tuning the material properties of graphene and VO2. The metal-insulator transition of VO2 can be used to switch the spatial modulator from absorption mode to transmission mode, and graphene behaves as dynamically adjustable material for large scale absorbance and transmittance modulation. Below, we assume the conductivity of VO2 as 10 S/m and 200000 S/m for the insulating and metallic states, respectively.
3.1 Spatial modulator with single-layer patterned graphene and VO2
When the VO2 is in the metallic state and graphene µc = 0.8 eV, the reflectance, transmittance, and absorbance spectra of the proposed modulator under the normal TE-polarization incidence are shown in Fig. 3(a). From the absorbance spectrum (the red curve), we observe that the modulator’s over 85% absorbance is ranging from 1.33 to 2.83 THz with the center frequency of 2.08 THz and a fractional bandwidth of 72.1%. The transmittance (the green curve) is close to zero in the whole frequency range because VO2 acts as a metallic mirror in the conducting state. Because of the gradient width of ginkgo-leaf patterned graphene, continuous plasmon resonances over a wide terahertz frequency range can be excited, and broadband terahertz absorption or transmission properties of the modulator can be achieved. The absorbance phenomenon can be further interpreted by the interference theory, which is an effective theoretical interpretation based on interference for metamaterial absorbers [58–59]. The simulated result (red curve) and the calculated result from the interference theory (blue curve) are displayed in Fig. 3(b), showing a good agreement with each other. To better understand the physical origin, we plot the electric field (|E|) and magnetic field (|H|) distributions of the modulator on the xoy plane at the absorbance peak frequency of 2.25 THz, the 50% absorbance frequency of 3.20 THz, and dip absorbance frequency of 3.95 THz in Figs. 3(c)–3(h), respectively. As clearly shown in Fig. 3(c), most of the electric fields are strongly confined on the edge of the ginkgo-leaf patterned graphene sheet due to localized surface plasmon resonance at 2.25 THz corresponding to the near-unity absorbance. While the electric fields are significantly decreased at 3.20 THz (Fig. 3(d)) and without showing obvious resonance at 3.95THz (Fig. 3(e)), which agree well with the half and 7.4% terahertz absorbance, respectively, shown in Fig. 3(a). From the magnetic field distributions shown in Figs. 3(f)–3(h), we find that the magnetic fields are strong at 2.25 THz, decreased at 3.20 THz, and very weak at 3.95THz, which are consistent with the electric field (|E|) distributions shown in Figs. 3(c)–3(e).
Fig. 3. (a)Reflectance, transmittance, and absorbance spectra for σVO2 = 200000 S/m and µc = 0.8 eV. (b) Comparison of the calculated and simulated absorbance spectra. (c), (d), and (e) are electric field distributions at 2.25, 3.2, and 3.95 THz, respectively. (f), (g), and (h) are magneitc field distributions at 2.25, 3.2, and 3.95 THz, respectively.
Then, we investigate the broadband modulation performance of the proposed modulator under the absorption mode and transmission mode below. The modulation depth is defined as ηA = (Aon – Aoff)/Aon for absorption mode and ηT = (Ton – Toff)/Ton for the transmission mode. When the VO2 is in the metallic state with the conductivity of 200000S/m, the modulator behaves as a tunable absorber. The absorbance spectra can be dynamically adjusted via µc of graphene by controlling the gate voltage Vg, as illustrated in Fig. 1. Figure 4(a) displays the dependence of absorbance A on the frequency f and µc under normal TE polarization incidence. It is clear that the peak absorbance at 1.95 THz continually increases from 24.3% to near 100% as µc increases from 0 to 0.8 eV, and the corresponding terahertz absorbance modulation depth of 75.7% is achieved. Figure 4(b) shows the modulation depth of absorption mode. are plotted and compared in Fig. 4(c). Clearly, the broadband absorbance modulation depth ηA over 50% in 0.28-3.50 THz with the maximum terahertz absorbance modulation depth of 84.8% is achieved at 2.80 THz. On the other hand, when VO2 is in the insulating state with the conductivity of 10 S/m, the transmittance of the modulator at 2.5 THz continually decreases from 87.0% to 35.5% as µc increases from 0 to 0.8 eV, as shown in Fig. 4(c). The modulation depth of transmission mode is plotted in Fig. 4(d). It is found that the transmittance modulation depth ηT over 30% in 0-3.34 THz with the maximum terahertz transmittance modulation depth of 59.2% at 2.5 THz is achieved in this modulator design. Therefore, the proposed modulator demonstrates good performance for both the absorption and transmission modes, which may have potential applications in various smart tunable terahertz optoelectric devices.
Fig. 4. (a) Absorbance spectra under different graphene chemical potential µc when VO2 is in the metallic state. (b) Modulation depth for µc switching from 0 to 0.8 eV under absorption mode. (c) Transmittance spectra under different µc when VO2 is in the insulating state. (d) Modulation depth for µc switching from 0 to 0.8 eV under transmission mode.
3.2 Spatial modulator with three-layer patterned graphene and VO2
To further increase the modulation bandwidth, a spatial modulator composed of three-layer patterned graphene and VO2 is proposed, as showed in Fig. 5(a). In this design, three graphene layers from top to bottom are patterned with a cross, carved square, and ginkgo-leaf-shape. Three Topas spacers with thicknesses of h1, h2, h3 are sandwiched among the graphene layers and the backed VO2. The detailed geometric parameters are shown in the caption of Fig. 5(a). By merging the multi-resonance mode of the three-layer patterned graphene in the design, the bandwidth of the modulator can be broadened significantly. As shown in Fig. 5(b), the modulator has an excellent broadband terahertz absorption property with over 85% absorbance bandwidth of 3.13 THz ranging from 0.77 to 3.90 THz for the VO2 in the metallic state and µc = 0.8 eV. The corresponding fractional bandwidth increases to 134.0%, which is much higher than that of 72.1% of the modulator with monolayer graphene and VO2.
Fig. 5. (a) Schematic diagram of the proposed broadband spatial modulator with three-layer graphene and VO2, where h1 = 25 µm; h2 = 9 µm; h3 = 14 µm; a = 10 µm; b = 52 µm; s = 0.1 µm; c = 26 µm; d = 13 µm. (b) Absorptance spectra of the proposed broadband spatial modulator with single/three-layer graphene and VO2.
The broadband modulation performance of this spatial modulator with three-layer graphene and VO2 are studied. When VO2 is in the metallic state with the conductivity of 200000 S/m, the spatial modulator acts as a tunable absorber, and its maximum terahertz absorbance modulation depth reaches 86.5% for µc switching from 0 to 0.8 eV at 2.50 THz, as shown in Fig. 6(a). When VO2 is in the insulating state with the conductivity of 10 S/m, as shown in Fig. 6(b), the maximum terahertz transmittance modulation depth of 80.5% for µc switching from 0 to 0.8 eV at 2.08 THz is obtained. As shown in Fig. 6(c), the broadband spatial modulator has an absorbance modulation depth of over 50% in 0.18-4 THz for the absorption mode and the transmittance modulation depth of over 50% in the whole frequency range for the transmission mode are achieved. To explore the full potential of the modulation depth of the modulator under transmittance mode, we study the dependence of the transmission spectra on different conductivity of VO2 while maintaining graphene µc = 0 eV, as shown in Fig. 6(d). It is observed that the peak transmission continually increases from 0 to 91.2% as σVO2 decreases from 40000 to 10 S/m at 1.80 THz, demonstrating excellent terahertz transmittance modulation depth approaching 100% in the whole frequency range with changing only three orders of VO2 conductivity. In addition, we also investigate the absorbance modulation of modulator under different conductivity of VO2 while maintaining graphene µc = 0 eV. The modulation performance of the proposed modulators under absorption and transmission modes are summarized in Table 1.
Fig. 6. (a) Absorbance spectra under different graphene chemical potential µc when VO2 is in the metallic state. (b) Transmittance spectra under different graphene chemical potential µc when VO2 is in the insulating state. (c) Modulation depth under absorption and transmission modes for µc switching from 0 to 0.8 eV. (d) Transmission spectra under different VO2 conductivity when all graphene chemical potential µc are set as 0 eV.
Table 1. Performance of the proposed spatial modulators based on patterned graphene and VO2
4. Conclusion
In conclusion, we have proposed a variety of broadband spatial modulators composed of hybrid patterned graphene and VO2, which can realize switchable absorbance and transmittance modulation with the same structure. For the spatial modulator with a monolayer ginkgo-leaf patterned graphene and VO2 has the fractional bandwidth of over 85% absorbance is 72.1%. And the maximum absorbance and transmittance modulation depth of 84.8% and 59.2% can be achieved as the graphene Fermi level increases from 0 to 0.8 eV. To broaden the modulation bandwidth of the modulator, three-layer patterned graphene and VO2 are introduced in the modulator design, and the fractional bandwidth over 85% absorbance is enhanced to134.0%. And, the maximum absorbance and transmittance modulation depth of 86.5% and 80.5% are obtained. The transmittance modulation depth can be further enhanced to 100% in the whole frequency range by changing VO2 conductivity under transmission mode. The proposed modulator demonstrates good performance for both the absorption and transmission modes, providing great potential in tunable terahertz optoelectric devices.
Funding
Shenzhen Science and Technology Projects (JCYJ20180306172733197); China Scholarship Council (201906315036); State Key Laboratory of Millimeter Waves (K202101).
Disclosures
The authors declare no conflicts of interest.
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